Question

let S={2,4,6,8}.The operation * on S as follows;if x and y are any elements of S x*y means the remainder when the result of multiplying x by y is divided by the inverse of 6.​

Answer 1

The * operation on S is defined as the remainder when the result of multiplying two elements of S is divided by the inverse of 6.

Step-by-step explanation:

Let's define the operation * on S. If x and y are any elements of S, x*y means the remainder when the result of multiplying x by y is divided by the inverse of 6. We can calculate the result of x*y using the formula:

x*y = (x * y) % (1/6)

For example, if we take x=2 and y=4, the calculation would be:

2*4 = (2 * 4) % (1/6)

Since 2 * 4 = 8 and the inverse of 6 is 1/6, we can simplify the calculation:

2*4 = 8 % (1/6)

Now, we need to find the remainder of 8 divided by (1/6). To do this, we can multiply 8 by 6, which gives us 48, and find the remainder when dividing 48 by 1:

2*4 = 8 % (1/6) = 48 % 1

Since 48 divided by 1 leaves no remainder, the result is 0:

2*4 = 8 % (1/6) = 48 % 1 = 0